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Chaos, Quantum-transactions and Consciousness
A Biophysical Model of the Intentional Mind
Chris King
Mathematics Department
University of Auckland
_______________________________
Abstract: The nature of subjective conscious experience, and its consequences in intentionality, remain the
central unsolved problem in science and one of critical importance to humanity’s future as sentient observers
and autonomous participants in a world history we are coming to have ever more pivotal influence upon. Each
of us who read this paper are subjective conscious observers, making an autonomous decision to carry out a
volitional action. All our knowledge of the physical universe is gained through the immediate conduit of our
subjective experience and our intentionality in turn has major impacts on the physical world around us.
To understand how the subjective aspect arises requires both a radical investigation down to the foundations of
physics and an understanding of how subjective awareness, as opposed to mere computational capacity, may
have become elaborated by Darwinian natural selection. We thus have to find reasons why subjectivity itself,
rather than computation alone, is of pivotal importance in organismic survival. The answer lies in its capacity
to anticipate situations crucial to survival. For this to be possible, the foundations of physics must contain a
principle of space-time anticipation not covered by any mechanism of computation alone, or subjectivity would
become superfluous and would have never been selected for in evolution. This paper sets out to demonstrate
how quantum transactions universal to all quantum phenomena my fulfil this pivotal role.
The role of dynamical chaos1 and bifurcation2 in neurodynamics has been the subject of an increasing volume of
theoretical and experimental research in which transition from chaos to order may form a key process in
perception and cognition. There has also been a continuing interest in the possible link between quantum nonlocality3 and consciousness. This paper presents a two-part theory in which: (a) a fractal link between
neurodynamical chaos and quantum non-locality; and (b) a complex system theory of the sub-quantum world;
together provide a physical solution to the mind-brain paradoxes of subjective consciousness and free-will.
The fractal link between dynamical chaos and quantum uncertainty is proposed to be made through overlapping
non-linearities capable of chaos, running from the neurosystems level down through the neuron, synapse, to the
ion channel. Chaotic systems possess sensitive dependence, and brain states also contain features of selforganized criticality. In a critically poised brain state representing uncertainty of outcome, it is proposed that
sensitive dependence opens the brain to quantum processes. In the transactional interpretation of quantum
mechanics, future states form part of the boundary condition of reduction of the wave packet4 . Transactional
supercausality may allow a form of prediction in the excitable cell which bypasses and complements formal
computation. The selective advantage of such a process would explain the emergence of consciousness in
organismic evolution (King 1996a, 1996b).
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1
Introduction
The nature of subjective consciousness and its relationship with brain function remains the most challenging
problem facing modern science, and one whose principles remain elusive, despite major conceptual advances in
1
A chaotic system is arbitrarily sensitive to initial conditions, mixes spatial regions, and has a dense set of periodicities.
2
A sudden change in dynamical structure resulting from a continuous change in the underlying parameters.
3
The capacity of a quantum system to maintain a global coherence between all regions of its wave function when the
state of any of its particles is subjected to measurement.
4
The reduction of the set of probabilities in any quantum prediction to a single realized outcome.
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other fields. This suggests a progress in understanding the mind-brain relation requires a further biophysical
discovery. This paper presents a model in which chaos and novel quantum mechanical principles combine to
give a physical description in which mind can interact with brain and in addition provide a potential predictive
advantage of evolutionary significance for the organism.
The possible involvement of chaos in consciousness has been raised by a variety of researchers from Skarda and
Freeman (1987) to Hardcastle (1994) and in several of my own papers King (1991, 1996) based on the usual
process of neurons, synapses, and ion channels. Hameroff (1994) has also discussed the potentiality of
microtubules5 to use Bose-Einstein condensates6 as a quantum computer7 possibly in the form of cellular
automata8 operating on the microtubule’s protein subunits, coupling these to global brain states through
coherence9 .
The current model also develops from properties of the single cell but utilizes the central electrochemical
properties of cell membrane excitations, broad neurodynamical features including coherence and chaos, and a
potentially predictive property of quantum-nonlocality universal to all quantum interactions.
The model consists of two parts:
(1) A polyfractal linkage between chaotic neurosystems, the excitable cell, and the molecular level of the
synapse and ion channel. Rather than being a simple self-similar process, this linkage involves biological
structures with fractal dynamics which interact on a discrete series of descending scales, neurodynamic, cellular
and molecular.
(2) A transactional interpretation of quantum mechanics, providing a space-time supercausality, which may be
able to be utilized by the excitable cell, and consequently the dynamical nervous system, to provide an implicit
form of anticipation of events which complements the predictive capacity of formal computation.
The paper is organized as follows: 2: The problems of consciousness and free-will. 3: A synopsis of the
polyfractal and supercausal aspects of the model. 4: The polyfractal linkage between global neurodynamics,
cellular and molecular levels. 5: Transactional supercausality as a basis for implicit anticipation in the excitable
cell and brain. 6: Evolutionary origins of chaos and consciousness. Supporting evidence and detailed theory are
postponed to the appendices so that the general reader can more easily understand the overall nature of the
model. Appendix A: Fractal neurodynamics. Appendix B: Quantum mechanics and transactions. Appendix C:
The role of global brain structures in consciousness. Experimental evidence remains suggestive rather than
conclusive because of limitations of the current state of experimental research.
2
Consciousness and free-will: Two aspects of the subjective mind
The subjective mind presents both an existential dilemma and a two-fold interactive problem in relation to the
physical world. While consciousness research has become a fashionable scientific area, the inverse interaction,
free-will, raises acute scientific problems, because it invokes the spectre of causal interference in the physical
determinism required for computation in the brain. In this paper I will advance a complementarity perspective in
which mind and universe are aspects of a complementary totality. The supercausal theory will solve the mind-
5
Subcellular organelles, forming subunits of the eucaryote flagellum, spindle apparatus of chromosome separation and
serving cellular structural and transport functions.
6
Many particles [bosons] existing in one wave function, illustrated by the laser and superconductors.
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A formal computer using superimposed quantum states rather than discrete states.
8
A simple algorithm evaluating the state each cell in a grid in terms of its neighbouring states.
9
Two oscillations are coherent if their waves match phase, e.g. laser light.
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brain paradox in so far as it provides a physical explanation supporting an interaction between mind and brain.
Subjective consciousness remains qualitatively distinct from and complementary to any objective description of
its possible role, whether by transactional or other means.
Because consciousness and free-will are subject to multiple interpretations, I will make the following informal
definitions:
Consciousness – Brain acts on mind: subjective awareness accompanying attentive brain function.
Free-will
– Mind acts on brain: mental will, or intent, acting on brain function.
2.1 The primacy of subjective consciousness
Although scientific description is based exclusively on the physical universe, our contact with reality is entirely
through our subjective experience, whose consensus of stable representations we assemble into the physical
world view. This subjective aspect of reality is often referred to as the conscious mind. Because its subjective
nature makes it unavailable to objective investigation, reductionist descriptions identify it merely with functional
attributes of the brain, inferring computational machines might also possess consciousness. However it remains
unclear whether a physical universe without conscious observers could exist in any more than a purely
conceptual or theoretical sense. Subjective consciousness may be necessary for the actualization of physical
reality, and thus fundamental to physical existence (Barrow & Tipler 1988).
The conscious mind can also be described functionally as an internal model of reality. While such an explanation
does not address the basis of subjectivity, it does help explain some of the more bizarre states of consciousness and
is supported by many actively constructive aspects of sensory processing. Such an internal model can be described
in terms of dynamical brain processes which undergo unstable transitions to and from chaos. Dynamical resonance
also provides a direct means to solve the ‘binding problem’, how the unitary nature of mind emerges from
distributed parallel processing (Hardcastle 1994).
2.2
The causal paradox of free-will
A second critical property of mind comes into play as we move from perception into action. To quote Sir John
Eccles : ”It is a psychological fact that we believe we have the ability to control and modify our actions by the
exercise of ‘will’, and in practical life all sane men will assume they have this ability” (Hooper & Teresi 1986).
However this premise, which is basic to all human action, contradicts physical determinism, because any action
of mind on brain contradicts the brain functioning as a deterministic computational machine.
A confluence of ideas between quantum physics and the science of mind may resolve this apparent paradox.
Firstly physics has difficulty determining when collapse of the wave function from a set of probabilities into an
actual choice takes place, leading to some interpretations in which the conscious observer collapses the wave
function. Secondly quantum uncertainty and non-locality provide exactly the types of explanation which could
enable the subjective experience of free-will to be consistent with a non-deterministic model of brain function.
The unpredictability of chaos could in turn provide a means to link quantum indeterminacy to global brain states.
3
The polyfractal-supercausal model: a synopsis
3.1
The chaotically-excitable cell
Chaotic excitation may have provided key advantages for the first cells, including sensitivity to light, vibration
and chemical factors, through sensitive dependence on initial conditions, the capacity to generate
electromagnetic fields and use them to sense other cells, to respond to internal changes and to utilize bifurcation
in cellular decision-making.
A chaotic or unstable system can dynamically inflate arbitrarily small perturbations into global fluctuations. In
the case of the cell, the underlying limit of such perturbations is the molecular level of the quantum. A cell in a
chaotic state, or tuned to its own threshold of excitation could thus in principle be sensitive to a single quantum,
as is the case for retinal cells fig 4(a). This could result from opening of an ion-channel, the release of a single
synaptic vesicle or other processes. The effects of a single quantum fluctuation could thus become inflated into a
burst of excitation of the cell.
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Transactional supercausality asserts that all quantum wave reductions possess an anticipation of the future state
of their absorbers, providing an implicit form of prediction in a sensitively excitable cell. By coupling related
emissions and absorptions, the chaotically excitable cell may have thus gained access to anticipatory information
about its immediate environment, providing a critical evolutionary advantage.
3.2
The polyfractal brain
The idea is that this evolutionary advantage is then incorporated into the nervous systems of multi-cellular
organisms, in which parallel organization, chaotic excitability and the capacity for coherence provide for the
expansion of the existing cellular properties into global neurodynamics. The excitable cell, rather than neural net
architecture alone, thus becomes pivotal in the evolution of the conscious brain.
The brain is conceived of as a polyfractal, a fractal complex of three distinct units: global neurosystem, cell and
molecular complex, each capable of controlled chaos and interlocked structurally by a change of scale. Each is
linked so that neurodynamical instabilities can be influenced by cellular instabilities which in turn can be
influenced by quantum instabilities. Reciprocally, the nature of the global neurodynamic determines which cells
are critical and each neuron can determine by its excitation and adaption which molecular organelles may be
critical. This would provide a mutual scale interaction between global and quantum events.
The fractal branching structure of the neuron supports many-to-many connectivity enabling each successive
processing stage to be an integral transform17 of the preceding one, just as a hologram is a many-to-many
representation of an image. Models of the nervous system have been proposed in which neural layers develop
chaotic excitation modulated by attention, with the capacity to represent each perception in a distributed manner
across the cortex through phase coherence, again leading to spatial coherence within temporal chaos and
bifurcation, as in the case of the cell.
In using controlled chaos, the brain could link the instabilities of neurosystem, cell and molecular complex so
that choice is made by an inflated quantum reduction. Such instabilities can complement formal computation
because they correspond to heuristic choices31, where computation anyway becomes probabilistic. It the brain
uses global instabilities in the transition from chaos to order, unstable resonances may become linked with
quantum anticipatory excitons. Again here there is a structural complementation between quantum computation
and transactional exchange. The complex connectivity of the brain could then enable its global dynamics to
provide a new emergent manifestation of quantum non-locality, reflected in turn in the form of subjective
consciousness.
3.3
The interactive mind
The conscious mind would thus gain an anticipatory role in brain function, corresponding to the indeterminacies
of the sensitively unstable brain. Free-will also gains a role, providing the choice made through collapse of the
wave function. While an unstable brain might seem problematic, in dealing with the ‘real’ world, such
instabilities are confined to sensitively forming a perception and making a decision already characterized by
external circumstances. They are thus just those instabilities an active conscious mind requires.
4 Linking chaos and quantum mechanics.
Chaotic systems possess sensitivity to initial conditions and computational unpredictability, (Schuster 1986,
Stewart 1989) because arbitrarily small perturbations exponentiate with time into global instabilities, the ‘butterfly
effect’10 . Sensitivity makes a chaotic system responsive. It also prevents a chaotic system from being predicted
because infinitesimal errors exponentiate. It is thus impossible for an observer outside the system to describe it
precisely enough to predict its outcome. The mixing property of chaotic systems results in states which permeate
phase space11 . They also generally contain an infinite number of distinct periodicities forming a rich internal
10
As originally described by Lorenz, a butterfly flying in Hawaii could trigger a subsequent hurricane elsewhere in the
Pacific.
11
The space of internal configurational states of a dynamical system.
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structure which can be revealed by bifurcation out of chaos. Often this internal structure takes the form of a selfsimilar fractal, which may be an attractor12 , repeller or other invariant set. Fractals characteristically repeat their
structure on ever diminishing scales, displaying a power law relation from which a non-integer fractal dimension
can be derived. In the polyfractal model, global neurosystem, cell and molecular complex , are linked so that they
have mutually interactive instabilities.
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Fig 1: Chaotic neurosystems dynamics is illustrated by: (a) Time evolving EEG with broad frequency spectrum and
associated correlation dimensions. (b) The low correlation dimensions of a variety of brain states. (c) Phase portrait of
an EEG recording (Babloyantz & Salazar 1985). (d,e) Chaotic and distributed processing is combined in Walter
Freeman's model of olfactory bulb processing. Recognition of a given odour by the bulb arises from the distributed
pattern of activity, occurring in bursts phased with inhalation. The time-dependent dynamics supporting this consists
of bifurcation from low-level chaos to higher level activity which settles into an existing attractor [recognition] or
develops a new one [learning] after exploring phase space in higher level chaos. Chaotic neural nets based on
neuroanatomy can perform pattern discrimination tasks competitively with other neural net designs (Skarda &
Freeman 1987). (f) Phase decoherence in novel or unexpected stimuli is consistent with a distributed model of
processing based on oscillatory phase, similar to a hologram.
NOTE: All diagrams are digitally processed by the author. Original sources are indicated in the text or captions.
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Fig 2: (a) Chay-Rinzel model (1985). Period 3 oscillations in Nitella indicate dynamics within the chaotic regime.
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A conserved set of states towards which all neighbouring states converge.
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(b) Period doubling bifurcation in model. (c) Experimental behaviour of voltage gated K+-channel is consistent
with a fractal model (3) rather than a one, or two step Markov chain (1,2) (Liebovitch et. al. 1987a,b). (d) Fractal
dynamics of the excited muscle oxygen carrier protein myoglobin is illustrated in term of functionally important
movements and equilibrium fluctuations involving a variety of quantum transitions on differing scales.
4.1 The scale link between neurosystems and cellular dynamics.
Appendix A outlines evidence for chaos and bifurcation in neurosystems, single cells and long-term adaption.
Evidence for chaos, fig 1, has been detected in the electroencephalogram for a variety of natural and pathological
states (a-c), although current techniques cannot distinguish chaotic and stochastic13 processes for active attention.
Freeman’s model of sensory perception (d,e) is based on spatially coherent oscillations which are chaotic in the time
domain, thus combining concepts of coherence, chaos and bifurcation in a single dynamical model. Transition to
high energy chaos accompanies inspiration, enabling the system to explore its phase space and avoid becoming
locked in any particular state. Reduction of the level enables the system either to fall into a learned attractor, or
bifurcate to form a new one in the case of a novel stimulus. The model is consistent with complex system
dynamics at the edge of chaos14 . The resonances of non-linear dynamics are capable of inducing the spatial phase
coherence, which accompanies recognition and orientation in experimental studies (f).
Freeman’s model has been traditionally applied to cell assemblies consisting of hundreds, or thousands of cells
whose individual behaviour may not reflect the global dynamic. However reciprocal coupling between major
cortical areas and individual neurons could provide the capacity for a global neurosystem dynamic, which is
unstable or chaotic, to become sensitive to instabilities in a single critical cell or synapse, which could consequently
be amplified into a global fluctuation or bifurcation15 .
Conversely the stability of single cells would be modified by the global dynamic. This situation naturally includes
decision-making processes in which critical states determine the outcome. Such fractal dynamics have been
explored in experimental models (Bower 1992, Teich 1992). The central nervous system includes reciprocal
linkages between neurosystem architecture and the single cell. One is illustrated in fig 5(b) where a single
hippocampal CA1 pyramidal cell has inputs from distinct brain regions, the sensoria and the reticular activating
system via distinct neurotransmitters and distinct anatomical regions of the cell.
4.2 The neuron as a fractal integral transform unit.
On a descending series of scales, the neuron is structurally and functionally a fractal processing system, fig 3, in
terms of its dendritic and axonic trees (b), and subcellular processing in dendritic microcircuits (d) and synaptosynaptic junctions (e). It is capable of unstable bifurcations and chaos, properties possessed neither by formal
McCulloch-Pitts neurons nor the analogue neurons in optimizing nets such as the Hopfield net (Tank & Hopfield
1987). Despite the approximate conformity to linearity of neuronal conduction over a restricted range above
threshold (ai), the neuron also displays self-organized criticality16 in the form of tuning to its sigmoid threshold
(aiii), limit-cycle bifurcation (aii), and chaotic dynamics as depicted by the Chay-Rinzel model, 7.1.2, fig 2(a,b),
and found in a variety of experimental studies.
The obvious sophistication of typical central nervous neurons, with up to 100,000 synaptic junctions, having a
13
14
A system based on repeated application of probabilities and random variables.
Both continuous dynamical systems and cellular automata display enhanced complexity, including production of
new structure and computational capacity [automata] when their parameters are close to, or traverse the boundary
between chaos and order. Publications of the Santa Fe Institute discuss a variety of complex systems (e.g. Jen 1990).
15
This would effect only the existing instability, i.e. a single decision-making step at an uncertain point in
computation.
16
A system which converges to a critical state. Threshold tuning takes the neuron towards critical sensitivity.
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variety of anatomical forms fig 3(c), contrasts markedly with artificial neurons and nets. The variety of up to 12
distinct modes of locomotion of hydra, which has an undifferentiated nerve net, illustrates that complex behaviour
may arise as much from cellular sophistication as from neural net complexity. Single-celled protozoa also display
behavioural complexity, leading to the conclusion that subcellular organelles can coordinate and process
information.
The fractal aspect provides the neuron with its second outstanding complex systems feature, that of a fractal
integral transform17 , as exemplified by the Fourier transform of the hologram. The many-to-many nature of the
synaptic contacts arising from the neuron’s fractal structure, when organized in layers enables the sequential
formation of complex sensory fields and modular cortical regions fig 6. Oscillatory phase fronts allow for
coherence and transform inversion supporting the retrieval of previous states in the form of a hologram as suggested
by Pribram (1971) and consistent with decoherence in experimental studies fig 1(f).
4.3 Subcellular organelles, the scale link between cell and molecule.
Cell organelles can similarly provide a fractal link between cellular and molecular dynamics. The dynamics of the
synapse fig 3(e) and membrane involves a rich diversity of non-linearities including quadratic sensitivity in touch
receptors and bilinear dynamics in synapto-synaptic junctions, both of which can be chaotic.
In cortical synapses, there is no need for the large number of vesicles seen in the neuro-muscular junction. It has
been proposed that in some cortical synapses, the release of the contents of a single vesicle is sufficient to traverse
the threshold and elicit a post-synaptic response. A vesicle, releases around 10,000 acetyl-choline molecules,
activating 2000 ion channels, causing discrete micro-potentials even at the neuro-muscular junction, which
depolarize the membrane by about 1 mV, sufficient to result in an action potential if a cell is already at threshold,
making it dynamically feasible for unstable fluctuation at the level of the synaptic vesicle to precipitate cellular
instability and subsequent global neurosystem bifurcation.
Eddington (1935) and Eccles (1970) discussed the possibility of quantum-mechanical action of the vesicle and
pointed out that the uncertainty of position of a vesicle of 400 oA diameter and mass 3 x 10-17g is about 30oA,
comparable with the thickness of the membrane. Because of this, the vesicle can be regarded as a quantum object,
which is at the same time capable of triggering cellular and hence global instability. The topological closure of the
vesicle membrane thus results in the amplification of quantal instabilities from the level of the molecule to the
larger level of the vesicle. The kinetics of vesicle association with the pre-synaptic membrane is determined by
protein binding, making vesicle release a function of the kinetics of a single molecular complex.
Concentration dynamics is linear only for single molecule interactions, but ion channels such as the acetyl-choline
channel require two molecules for activation, again having quadratic dynamics. In the fractal model of ion channel
kinetics Liebovitch (1987a), as discussed in appendix A, fig 2(c), molecular conformation changes occur fractally
on scales varying from larger functionally important global changes to a variety of smaller thermodynamic
fluctuations. Large protein molecules are thus both structurally and functionally fractals. The chaotic nature of
quantum kinetics, fig 4(h,i) finally allows the neurodynamic interface with the level of the quantum. Microtubules
have also been proposed as functional cellular automata (Hameroff 1987, 1994) which could also be significant in
nervous function. Similar considerations apply to proteins which are responsible for vesicle release which, like the
microtubules, form a paracrystalline structure. Beck & Eccles (1992) have cited this interaction as a principal
vector for quantum stochasticity. Any of these structures could enable quantum fluctuations in a way which could
result in global neurodynamic changes.
17
The Fourier transform integrates the values of a function by multiplying each with an oscillating sine function to
form a frequency representation of the time-dependent function.
A hologram forms a physical realization through the
sinusoidal phase fronts of coherent laser light. Both act by a many-to-many integration process [each point on the
hologram corresponds to waves coming from every point on the image]. Each can be inverted to retrieve the original
form.
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4.4
Polyfractality
In the polyfractal model, global instabilities in brain dynamics are dynamically-linked to neuronal fluctuation.
Threshold tuning similarly enables neuron to respond unstably to synaptic perturbations. Quantization at the level
of the synaptic vesicle, ion channel and/or microtubule allows for capping off of the fractal process at the level of
molecular complexes. Amplification of quantum fluctuations into micropotentials at the neuronal level could thus
in principle, if the neurosystem is critically poised, lead to global bifurcation. Sensitive dependence and quantum
amplification make the brain theoretically able to detect fluctuation at the quantum level, consistent with the
sensitivity of sensory apparati which are all capable of detections at or close to single quanta, 8.1. It is thus
possible for chaotic dynamics at the global, cellular, synaptic and molecular levels to combine to provide a fractal
model in which global and quantum instabilities are linked by mutual interactions of scale.
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Fig 3: Non-linear and fractal aspects of the neuron. (a) Limit cycle at excitation threshold (ii) illustrates neuronal non-linearity,
despite approximate linear relation between depolarization current and firing rate in a limited range (i). Sigmoid transmission
curve (iii) and mechanoreceptive bulbs also have a non-linear response. (b) Fractal dimensions of dendrites of two cell types and
their electrodynamics (Schierwagen 1986). (c) Anatomical complexity of the neuron illustrated by the structural variety of
synaptic junctions, which also utilize distinct neurotransmitters. (d) Dendritic microcircuits and synapto-synaptic junctions (e)
place the level of net organization one or two levels below the neuron. Synaptic conduction involves many feedbacks, some of
which, including the two-molecule activation of the acetyl-choline ion channel have quadratic rather than linear concentration
dynamics.
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Fig 4: (a) Excitations of single rod cells show peaks with 0, 1, or 2 photons being registered, consistent with
quantum statistics of photons being released very slowly at a rate corresponding to the marks below (Bailer & Lamb ex
Blakemore 1991). (b) Feynman diagram of exchange of a photon, (c) higher-order diagram. (d) One-photon transaction
involves interfering offer and confirmation waves. (e) Electron deflection and positron creation and annihilation. (f)
Contingent emitters and absorbers as boundary of collapse.(g) Transactional reduction reduces to a combinatorial
problem. At first all emitters and absorbers are correlated. Afterwards only the selected pairs. (h) Electron traversing a
molecule has continuous variation of time [phase] with chaotic irregularity (i) (Gutzwiller 1992).
It is one thing to establish that fluctuations at the quantum level could become amplified into global instabilities in
the brain, but quite another thing to explain why the brain should find it advantageous to allow seemingly
disordered processes to intervene in its functioning. Normally noise is an anathema to computational precision.
How then could quantum-chaotic processes have been selected in evolution and utilized in nervous system
function?
5 Supercausality and the conscious brain
5.1
Transactions and correlations
Energetic interactions in the universe are based on real, positive energy particles. All quantum force field
interactions are mediated by virtual particles which depend on the existence of both emitter and absorber because
the exchanged particle can only be in existence for an interval determined by the uncertainty relations 8.3.2. A
virtual particle can become real if it is given a real positive energy18 , so real particles should behave likewise. The
strict rule which prevents a single real particle being accidentally absorbed at two different places in a spatially
extended wave function, indicates the absorber plays a significant role in wave function collapse, as do several
famous experiments in which changing the configuration of the detection apparatus after emission has occurred
changes the behaviour of the emitted particle (Horgan 1992). Heisenberg’s idea that quantum mechanics describes
our ‘state of knowledge’ of the system also places a formative emphasis on the detector as an absorber, in
determining the rules of quantum collapse in any measurement. All particles may thus arise and demise in like
manner out of the universe as a self-contained quantum system.
The transactional interpretation (Cramer 1986), appendix B, fig 4, is a formulation of quantum mechanics in which
the emitter and absorber impose mutual time-symmetric boundary conditions on quantum interaction. This means
that quantum non-locality, even in a one-particle wave function, is indirectly utilizing information about future
states19 of the universe in collapse of the wave function. The basis of the transactional interpretation is as follows:
The emitter radiates an offer wave indicating it can emit a photon. This offer wave permeates space-time. All
potential absorbers of the prospective photon throughout the universe at more distant and later times in turn radiate
similar confirmation waves indicating they can absorb a photon, but this wave radiates backwards in time, reaching
the emission vertex at the same instant the offer wave is radiated. The emitter is thus made aware of the existence
of all potential absorbers. Collapse of the wave function then results in reinforcement of only one of the many
potential absorbers. The mutual interference of the chosen offer and confirmation waves results in the wave
function of a real photon travelling between the chosen emitter and absorber.
18
Real particle interaction differs from virtual interaction in one important respect, all possible virtual particle
interactions happen simultaneously in force interaction, but in real particle interaction only a single quantum is
exchanged out of an envelope of possibilities, the choice of which constitutes reduction of the wave packet.
19
The transaction starts out in many worlds. The contingent absorbers may also be contingent future states of other
interactions, existing only as a probability in terms of quantum mechanics. However in the completed transaction,
which happens for the emitter as soon as emission occurs, the existence of the absorber is certain. The collapse of any
wave packet is thus a collapse of the universal wave function. The entire historical process is a single collapse
appearing in serial time, but actually occurring throughout space-time in a supercausally-coupled event, the ‘infinite
clockwork’ of Maria Sabina (22).
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20
The advent of Bell’s theorem and the pair-splitting experiments of Aspect et. al. (1982) among others, have
demonstrated that in a splitting to form a quantum-correlated particle pair, non-locality ensures that, although
neither is in a specific state to start with, when the state of one of the particles is measured, the other is immediately
determined to have a complementary state. Although the information at each particle detector appears random,
there is actually a correlation between the statistics of the two detectors which demonstrates non-locality. Because
we can detect the correlation only when we examine both detectors, we cannot use the process to explicitly transfer
information faster than the speed of light.
1980) of the sub-quantum world.
The information is enfolded in the hidden21 implicate order (Bohm
5.2
Transactional supercausality and quantum inflation
Transactional supercausality or transcausality (King 1989) proposes a theory in which the temporal ordering of
causal events is replaced below the quantum level by symmetric space-time transactions forming a hidden complex
system. Rather than being random, quantum indeterminacy would arise from a non-local pseudo-random22
process. Because future states are part of the boundary conditions, a transaction cannot be reduced to a
deterministic process in terms of increasing time23 . The absorbers may exist only as future probabilities arising
from other future quantum interactions. A paradox in temporal determinism results. Transactional collapse thus
carries predictive information in implicit form, which could be accessed by the emitter, for example through
resonant excitations in which the brain emits and reabsorbs its own excitons.
In chaotic systems, sensitive dependence on arbitrarily small perturbations makes it possible for fluctuations on the
quantum scale to eventually become amplified into global differences, something I will call quantum inflation. The
interpenetration of classical and quantum chaos at the level of molecular kinetic processes24 forms the lower scale
limit where chaos and quantum non-locality merge, 8.4. This means that the underlying source of ‘randomness’ in
kinetic processes is also quantum indeterminacy. In fact this is clear from quantum mechanics, in which evolution
of the wave function is deterministic and reduction of the wave packet is the source of all natural ‘randomness’25 .
Since every natural stochastic process can thus be traced ultimately back to indeterminacy, transcausality may apply
to a variety of evolutionary and historical processes.
A more systematic form of anticipation could arise from parallel transactions which may provide anticipatory
20
Bell’s theorem placed limits on the correlations between two particles in a single wave function if they were related
in a local and causal manner. Experiments, including Aspect et. al. (1982) proved correlations exceeded these bounds,
confirming the intrinsic non-locality of quantum mechanics.
21
22
Bohm (1952) originally described such sub-quantum theories as hidden-variable theories.
A [super]causal process is pseudo-random if successive values approximate those of a random distribution in that all
values are equi-probable and there are no dominant periodicities. A system with many interacting parts such as a
classical gas may return pseudo-random measurements because the position of any particle is a function of the positions
of all the others.
23
It is thus neither random nor predetermined, providing consciousness with a critical role.
This is a double-edged privilege however, as responsibility takes on cosmological proportions!
24
Kinetic interactions of an electron with a molecule are an experimental example of quantum chaos, fig5(c).
25
Transactions would also explain the occurrence of causally unrelated coincidences, Jung’s synchronicity and the
stochastic basis of the I Ching (Wilhelm 1951).
Page 11
information in implicit form through correlated behaviour. The apparent randomness of quantum indeterminacy
may conceal other types of correlation more general than those seen in correlated pairs or multi-particle BoseEinstein condensates. It has been proposed that all particles in the universe are correlated by virtue of their
emergence from the common universal wave function. There may thus be many other types of correlation
occurring in the supposed randomness of quantum probabilities. Depending on the exact model for the correlations
envisaged, such a population could be a looser collection, such as a set of contingent emitters and absorbers, like
wave functions, or exchangeable particles.
A single cell with chaotic dynamic expressed globally via coherent excitation of the cell membrane might then
access a form of prediction unavailable through classical computation. A collection of cells forming a neural net
coupled in the form a global dynamical system could likewise experience linkage. The interaction could be based
on coherent oscillations or on the quantum sensitivities of a chaotic system undergoing bifurcation. A variety of
types of quantum exchange are possible such as photons, phonons or various excitons. The predictive interval
would be related to the lifetime of the exchanged quanta. Long-lived quanta or reverberations might thus prove a
predictive advantage. Emitters might function as quantum predictors for example through their interactive recoil
(Storey 1994). Major oscillations of the electro-encephalogram, especially in the 10 Hz-100 Hz range might also
form a basis for quantum linkage in the brain. Such oscillations could form a self-contained transactional system.
Global resonances might form Bose-Einstein condensates as they become coherent, although doubt has been cast on
the capacity of coupled molecular oscillators to do so Clarke (1994). Consciousness as a subjective manifestation
of quantum non-locality may thus possess a predictive capacity that, like the pair-splitting experiments, comes in an
implicate form which, although not formally computable, can emerge from an instability, subjectively experienced
as a hunch or intuition.
5.3 Representation of time in the cortex and in conscious experience
Since Grey-Walter first made subjects witness movement of a slide show via a motor cortex probe and found they
witnessed the slide change before they pressed a dummy button, the time properties of conscious experience have
been a conceptual challenge. Two experiments outline some puzzling temporal properties of consciousness. In the
first, (Kolers & von Grunau 1976) alternate lights of different colour flash for 150 ms with an intervening gap of 50
ms. Subjects report a single moving light which changes colour at the mid point, even on a first exposure, or
random colour change. This creates an apparent paradox because the colour change apparently occurs before the
second light has come on.
In a second class of experiment (Libet et. al. 1979), subject to repeated discussion (Libet 1985a,b,1987,1989,
Churchland 1981 a,b, Honderich 1984, Snyder 1988) involves the subjective timing of stimulation of one hand [say
the left, which excites the right somatosensory area] at the same time as direct stimulation of the opposite [left]
somatosensory area. The genuine hand-tingle is perceived before the cortically induced one even if it actually
occurred afterwards. Because of the considerable delay for the development of neuronal adequacy for the conscious
experience [200 - 500ms] the time of the experience appears to be referred back to the primary evoked potential
[10-20ms after stimulus]. Such temporal projection comes close to causal paradox. Libet comments “a dissociation
between the timings of the corresponding mental’ and ‘physical’ events would seem to raise serious though not
insurmountable difficulties for the ... theory of psychoneural identity”.
Dennett (1991) disavows such features as looping of the subjective time sequence out of the physical sequence,
because the order of consciously perceived events does not have to be coincident with the physical or apparent
physiological order when parallel processing builds up a global model of a time sequence from partial constructs.
This approach implies that the completed representation cannot be formed until after the sequence ends. It is not
clear this is the case with the first experiment.
As discussed in appendix C, the frontal cortex appears to be a distributed modular representation of intention and
action in the same way the sensory areas are for perception, including both the capacity to anticipate the outcome of
an evolving event and to utilize previous experience. Because it requires integration of past memories, present
experience and future intentions and survival strategies, and because its functional basis may be phase coherence,
our subjective internal model of time may more closely resemble a holographic image of space-time than merely a
mechanical representation of time based exclusively on past data. Damage to prefrontal areas effects predictive
sensory tracking tasks 9.4, in which the prefrontal cortex appears to utilize a modular representation of the phases of
Page 12
a predicted action. The separate processing of movement in visual perception constitutes a similar temporal
representation. A transform representation of time may provide better integration of past experience and future
needs in response to situational demands than a time-consuming computation based only on past data 6.1. It is
easy to see that visual perception constructs an external spatial reality, but is more difficult to accept time as a
similar internal construct, in which the subjective experience of free-will or intent arises because the function of
consciousness is to anticipate, forming an “ill-posed” problem in time whose outcome is not fully determined by
the initial conditions.
The central task of the brain is the representation of the activity of the organism in terms of past and future actions.
The likely basis for such a model is populations of dynamically coupled cells with chaotic excitation, bifurcating
into coherently oscillating populations which induce Hebbian26 reinforcement and hence synaptic adaption.
Although these may include forms of time-coding, possibly provided by the hippocampus, coherent oscillations
measure a circular phase-shift, i.e. an angle, and not a specific direction in time. Counting beats to determine
frequency or wavelength also requires a reciprocal time or distance corresponding to the uncertainty relations,
8.3.327 . The use of coherence is thus formally equivalent to quantum measurement. Quantum decoherence has
also been proposed as a basis for wave function collapse (Zurek 1991). Cortical oscillations and their
corresponding mental states may thus be inflated quanta reverberating through the brain. The subjective experience
of the present may consequently be an extended quantum of the present, forming an envelope of immediate past and
future states linked by transaction. This coincides with the way we generally deal with the present as a contextual
flow of events linking past and future in integral attention spans of around half to one second duration.
When the the attention process is fixed on itself and sensory and/or cognitive processes are suspended, a variety of
unusual reflexive mental states result, demonstrating that the mind is capable of self-generative behaviour in which
unusual anticipatory space-time properties have been reported. These include the bizarre subjective realities of
dreaming28 , lucid dreaming (La Berge 1990), sensory deprivation, meditative trance and hallucinogenic visions29 .
26
Hebb proposed that connected neurons which fire synchronously increase their synaptic strength.
27
The uncertainty Du in a frequency measured by counting beats against a known wave for time Dt is Dt. Du ≥ 1 .
Einstein’s law E = h.u immediately returns the uncertainty relation 8.3.3. This suggests quanta apply the same
discrete process.
28
Dreaming has been reported to have unusual space-time properties, associated as much with future as with past
experiences (Dunne c1935). Many traditional cultures report the use of dreams to anticipate future problems and
events. The dreaming state is not viewed as an illusory representation of the ‘real world’. In the shaman’s description,
the dreaming aspect of reality underlies the physical, so that the waking experience of the physical world is a restricted
aspect of a wider and more fundamental totality. After reading Dunne, I had a double nightmare that I was being
stung. I awoke at eight and told my wife the dream. At nine I was stung wide awake by a wasp. I have been chasing
the tail of that sting ever since! The night before I delivered a lecture on this subject at Oxford, I dreamed that I was
being attacked in the shoulder by nurses. Next morning, as a result of unexpectedly accompanying a friend to a doctor,
I was vaccinated in both shoulders by his nurses.
29
Five aspects of visionary states are noted in societies making ritual shamanic use of hallucinogens; geometrical
illusions, visions of animals and demons, separation of the mind from the body, clairvoyant visions of distant places,
and divination of past or future events (Harner 1973). “On the day following one ayahuasca party, six of nine men
informed me of seeing the death of my ‘chai’, my mother's father. This occurred two days before I was informed by
radio of his death”. The mushroom shamaness Maria Sabina avowed “The more you go inside the world of
teonanacatl the more things are seen. And you also see our past and our future, which are there together as a single
thing already achieved, already happened . . . Millions of things I saw and knew. I knew and saw God: an immense
clock that ticks, the spheres that go slowly around, and inside the stars, the earth, the entire universe, the day and the
Page 13
Such reflexive conscious states may show us deeper features of how the conscious mind interacts with quantum
supercausality than can be accessed from everyday waking experience, which is dominated by stable sensory
representations of the ‘classical’ macroscopic world. They may thus be a unique avenue to discovering the
implicate nature of quantum reality.
The problem of temporal representation is central to how attention and intention interact in the conscious moment.
Attention is intentional as well as perceptual. The problem of the “ghost in the machine” (Koestler 1967) is
essentially a problem of how such intentional attention is organised. As well as being an issue of control, this
problem may be paradoxical in terms of any mechanistic description, because the boundary conditions of
supercausality violate temporal determinism by including future states. The brain may thus be intuitively conscious
of the future in a manner prohibited from deterministic description with increasing time.
6 Evolutionary origins
6.1 The computational intractability of survival in the open environment.
The principal task of the brain of is to optimize the survival strategy most likely to enable the organism to evade
death and produce viable offspring. A computational problem is intractable if the number of computational steps
required grows super-exponentially with the complexity of the problem, or formally undecidable. The travelling
salesman problem (Bern & Graham 1989), finding the shortest route round n cities illustrates this, growing superexponentially.30 Many adaption-survival problems in the open environment are intractable because the number of
options in an open environment rapidly exponentiates, or undecidable because the problem becomes indeterminate.
Some intractable problems can be solved approximately by probabilistic methods. Neural nets also utilize random
fluctuations of gradually reducing energy to carry the net from local optima into a semi-global optimum. Chaotic
ergodicity may function similarly in biological neurosystems.
An active organism must complete a processing task within 0.1-1 second if it is going to have survival utility,
regardless of its complexity. This makes it clear why parallel processing is an integral feature of vertebrate nervous
systems. The modular features found in sensory processing realize a type of fractal algorithm (Penrose 1989,
Dewdney 1989) which in addition to parallelism, features fractal task assignment. Chaos and bifurcation provide
additional attributes of sensitive dependence, ergodic phase space pervasion, and the capacity to form new symbolic
structures through bifurcation.
A dynamical model for cognition would function as follows: The initial conditions determining a problem result in
an series of bifurcations generating accumulating attractors which form stable ‘symbolic’ representations of those
aspects of a problem which have been modelled. The complementary unstable component of the dynamic,
representing the unsolved aspects, continues to chaotically explore phase space, either bifurcating to stability, or
forming fractal and consequently quantum instabilities. The final resolution of such instabilities into a global
attractor determines the solution to the original problem. If either the initial conditions or subsequent bifurcations
prove incompatible, the dynamic may fail to cohere, precipitating a global rearrangement in which some of the
intermediate stabilities are removed or replaced.
Decision-making, which might be solved heuristically31 in a computer by making a random choice based on
probabilities, corresponds to an unstable system poised at bifurcation. This might correspond to two
interpenetrating assemblies of cells with differing coherent attractors, with a critical population of chaotically
desynchronised cells. Developing a new learned perception can be realized a little differently. The neurosystem
night, the cry and the smile, the happiness and the pain. He who knows to the end the secret of teonanacatl can even
see that infinite clockwork” (Schultes 1979, Guzman et. al. 1991,93).
30
Given two directions and n-1 choices for the second city etc. we have (n-1)!/2 steps, where n!=n.(n-1).(n-2). ...
.3.2.1
31
Inclusion of many possible strategies with probabilistic decisions based on success rates.
Page 14
enters high-level chaos, exploring its phase space and as the energy is reduced a bifurcation out of high-level
chaos occurs into a new lower level attractor. We thus have bifurcation out of chaos to form new structure.
Such indeterminacies can complement formal computation because the instabilities correspond to heuristic
choices where computation is anyway probabilistic. For the same reason any predictive capacity resulting from
transcausality complements formal computation.
6.2 Chaotic excitability as a founding eucaryote characteristic.
Chaotic excitability may originate deep in evolutionary history, representing one of the oldest features of
eucaryote32 cells (King 1978, 1990). Hameroff (1994) has suggested that microtubules may have provided a basis
for consciousness in single celled eucaryotes such as paramecium. While not wishing to under-play the
significance of microtubules, the current model envisages a more comprehensive basis for the origin of
consciousness in single celled eucaryotes centred around chaotic membrane excitation and its sensory potential.
This would apply to all eucaryote cells including ciliated and unciliated forms.
The Piezo-electric nature and high voltage gradient of the membrane provides an excitable single cell with a
generalized sense organ. Sensitive dependence would enable the cell to gain active feedback about the external
environment without becoming locked in a any mode. Excitation could be perturbed through photons, phonons or
weak bond interactions, making the membrane sensitive to light, vibration, and chemical stimuli. The effects of the
fluctuating fields generated by the excitations would provide an electromagnetic sense organ. The topological
closure of the cell membrane would provide local excitations with a capacity for coherence and global dynamics.
Bifurcation would also provide a global means for decision-making.
Such excitability would significantly predate the computational role of neural nets, making chaos fundamental to
the evolution of neuronal computing rather than emerging later from neural net organization. Chemical modifiers
may have included precursors of the amine-based neurotransmitters which span acetyl-choline, serotonin,
catecholamines and the amino acids such as glutamate and GABA, (Cooper et. al. 1982) several of which could
have a primal status chemically. The use of positive amines may have chemically complemented the negatively
charged phosphate-based lipids in modulating membrane excitability without requiring complex proteins (King
1990), supporting an early origin for excitability in the RNA era. Protein receptors could thus be a subsequent
adaption.
6.3 Consciousness as an evolutionary manifestation of chaotic neurodynamics.
In the supercausal model, an excitable cell, which evolved initially to achieve perceptual sensitivity or constrained
optimization through chaotic excitation, would also inherit a capacity for prediction through non-local quantum
interactions. This anticipatory capacity associated with quantum reduction would then constitute cellular
consciousness. The evolution of the excitable cell and subsequently the sensitively-dependent brain may thus have
been driven by the combined advantages of chaotic sensitivity and quantum anticipation.
Far from being an epiphenomenon, consciousness may thus have been been elaborated and conserved throughout
evolution, contrary to Jaynes (1976), because it has had survival value from the single cell to the brain. In the
evolutionary perspective, consciousness first developed as a cellular process and then evolved into a neurosystems
property as a result of global neurodynamical coupling of chaotically excitable nerve cells. Consciousness as we
know it is thus an emergent property of neurosystems which is already partially expressed in single cells. It is a
logical conclusion that the conscious brain has been selected by evolution because its biophysical properties provide
access to an additional principle of anticipation not possessed by formal computational systems.
The objective manifestations of consciousness and free-will are intrinsic to the quantum - a form of panpsychism.
Consciousness can be associated with a quantum by virtue of the capacity of the wave function to form a global
space-time model of the diverse features of the universe including its future states. Free-will is expressed in the
unique choice occurring in each reduction of the wave packet. Connectivity and coherence gives the brain a degree
32
All cells with nuclei, including protozoa, fungi, plants and animals are eucaryotes.
Page 15
of cooperative indeterminacy which is undeveloped in a single quantum, or a simple Bose-Einstein condensate like
a laser, leading to our contextually elaborate experience of consciousness and free will.
7 : Appendix A: Non-linear dynamics in the central nervous system
Experimental evidence for chaotic dynamics in a variety of aspects of central nervous system function has
accumulated in recent years. Chaotic has been experimentally detected both at the neurosystems level and in the
dynamics of single excitable cells, and ion channels have been shown to have fractal kinetics (King 1991).
Although these results provide circumstantial support for the model, experimental research cannot establish more
than suggestive consistency at this point in time.
7.1 Electrodynamics.
7.1.1 Neurosystems Dynamics: Evidence has been presented for chaos in the electroencephalograms of several
phases of cortical activity, including sleep, resting wakefulness and pathological states such as epilepsy (Babloyantz
1985, 1989, Basar 1990).
The low correlation dimensions33 of these states is consistent with chaotic
neurodynamics rather than stochastic, or locally programmed behaviour, fig 1(a,b). Active mental states have
slightly higher dimensions, consistent with both chaotic and stochastic models. Evoked potentials display
desynchronization on unexpected input, consistent both with cognitive instability, and with phase coherence being
utilized in recognition and orientation (Basar et.al. 1989, Hoke et.al. 1989), fig 1(f). Crick and Koch (1990,1992)
have suggested consciousness is associated with neuron populations associated by phase coherence in the 40 Hz
range, where there is evidence of attention-related change. Coherence is a property of non-linear systems.
The model of burst dynamics in the olfactory bulb advanced by Walter Freeman fig 1(d,e) combines these two
aspects into a single model based on bifurcations of the chaotic temporal dynamics of coherent spatially distributed
waves, which closely follows the neurophysiology and also permits real tests of pattern discrimination of neural
nets displaying comparable dynamics (Freeman & Baird 1987, Skarda & Freeman 1987, Freeman 1991, Yao et.al.
1991). In this model, low level chaos is lifted into a higher energy state by inspiration associated with an animal
sniffing. Chaos in this state then enables the system to explore its phase space, subsequently falling into an existing
attractor in the case of a recognised odour as the breath moves to expiration, or bifurcating to form a new attractor
in the case of a newly learned stimulus. The transition into chaos may thus provide sensitive dependence on input,
'randomizing' ergodic phase space exploration, parametric bifurcation to form new symbols, and possible quantum
amplification. Bifurcation from high-level chaos may in turn create new structures.
7.1.2 Single Cell Dynamics: Similar experimental evidence has accumulated for chaos in a variety of excitable cell
types, supported by the chaotic models of Chay and Rinzel (1985), fig 2(a,b). These extend the Hodgkin-Huxley
equations (1952) to take account of calcium ion pumping, displaying a variety of dynamical features, including
period doubling bifurcations and period three oscillations characteristic of the chaotic regime. Chaotic dynamics
well-model the excitations of Nitella pancreas cells and excitations in neurons and heart pacemaker cells. The
irregular behaviour of controlling cells in small ganglia such as in the mollusc Aplysia is also consistent with
sensitive dependence and chaos, by contrast with the more regular beating of subordinate neurons. Single-cell
chaos has also been recorded in both isolated and in-situ neurons.
7.1.3 Fractal Ion-Channel Kinetics : A Markov chain model is commonly used for ion channel kinetics34 , however
the likelihood that a closed channel will open behaves fractally with increasing time scales according to fig 2(c)
(Liebovitch et. al. 1987a,b, 1991). This is consistent with bio-molecular structures behaving fractally, not only in a
geometrical sense, but also dynamically as shown for myoglobin in (d) (Ansari et. al. 1985). The dynamics of many
important biological molecules may be fractal in this way, which involves the linkage between a variety of quantum
33
A dimension similar to the fractal dimension but based on relationships between pairs of points in the dynamic.
34
A stochastic model with a finite set of states with fixed transition probabilities.
In the Markov ion channel an open state is linked to one or more closed states.
Page 16
excitations of differing energies and scales, and feedback between tertiary structures and active sites.
7.2 Long-term adaption and development.
The developmental organization of sensory areas of the cortex appears to be dependent on sensory innervation and
stimulation, consistent with an attractor-bifurcation model founded on general genetic principles. The spatial
distributions corresponding to olfactory stimuli, fig 1(d) adopt new forms on relearning the same stimulus a second
time, consistent with bifurcation. Phase desynchronization of cortical evoked potentials is consistent with unstable
dynamics. Adaptive reorganization e.g. of ocular dominance regions on the cortex on covering a dominant eye, and
somatosensory barrels of the rodent on removing a whisker, indicate major sensory structures may arise as
dynamical systems induced through bifurcation.
8 : Appendix B : Quantum mechanics and transactions
8.1 Quantum sensitivity in the sense modes.
Limits on the sensitivity of nervous systems arise from quantum physics rather than biology. This is exemplified in
fig 4(a) by the capacity of retinal cells to record singe quanta, and by the fact that membranes of cochlear cells
oscillate by only about one hydrogen atom radius at the threshold of hearing, well below the level of
thermodynamic fluctuations. Moth pheromones35 are effective at concentrations at which only one molecule must
be active, as are the olfactory sensitivities of some mammals.
Despite the apparently similar electrochemical activity of their cortical areas, both the subjective natures of vision,
hearing, touch and smell, and their quantum modes, namely photons, phonons and weak bonding interactions are
qualitatively quite distinct. It is possible such modes may also function in the cortex in representing senses as
outlined in, 6.1. All could thus occur simultaneously in membrane excitation, resulting in synesthesia36 , in which
perception has cross-sensory effects. Hameroff (1994, p96) has suggested a similar sensory role for Bose-Einstein
condensates.
8.3 Quantum mechanics and wave packet reduction.
Quantum systems differ fundamentally from the classical case. While the time evolution of the system proceeds
according to a deterministic Hamiltonian wave equation, e.g.
( ∂2/∂ t2-—2 + m2 ) j = 0,
[8.3.1]
in the measurement process, reduction of the wave packet prevents a causal description because the probability
interpretation
[8.3.2]
P = j*. j
determines the limits on our knowledge of the system, resulting in a stochastic-causal model. Measurement
collapses the wave function from a superposition of possible states into one of these states. While quantummechanics predicts each outcome only as a probability, the universe appears to have a means to resolve each
reduction of the wave-packet uniquely, which I will call the principle of choice, the subject of Schrödinger's famous
cat paradox37 . The indeterminacy of [8.3.2] is also reflected in Heisenberg uncertainty
DE . Dt ~ h Dp x . Dx ~ h
2p
2p
in which we cannot know simultaneously all the dynamical aspects of a particle’s state.
[8.3.3]
Reduction of the wave packet in a measurement can most simply be described in terms of a system with a series of
distinct eigenvalues such as the energy levels of an atomic electron. The state of the system is represented by a state
35
Hormone-like sexual attractants detected by sense of smell during mating.
36
The experience of one sense, say a colour in relation to input of another sense, say a sound.
37
Quantum mechanics predicts a cat in a closed box which could be killed as a result of a radioactive decay is both
alive and dead with certain probabilities, while we find when we open the box it is only one : alive! or dead!
Page 17
vector |j which evolves in time according to the wave equation.
An observable quantity A is represented by an
operator with a set of eigenvectors {|jr}, with |j = ¬ar |jr. The probability (see 8.3.2) that an observation of A
will give the eigenvalue jr is
P=
S |· jr|jÒ| 2
[8.3.4]
Before measurement the state vector is |j, but afterwards it has collapsed to one of the eigenvectors |jr. Similarly a
photon in an interference experiment could be anywhere in its wave function, but is absorbed by one atom on the
photographic film.
8.4 Quantum chaos versus uncertainty as a substrate for classical chaos.
Repeated attempts to model a variety of quantum analogues of classical chaotic systems have revealed significant
differences which may inhibit the full development of chaotic dynamics in at least some of the quantum analogues
(Peterson 1991, Gutzwiller 1992). The wave aspect of the quantum effectively blurs the fractal structure and has
greater amplitude around the hidden periodic orbits. Such quantum inhibition may result in edge-of-chaos dynamics
consistent with quantum computation paradigms (Brown 1994). The particle traversing a molecule fig 4(h,i) gives
an illustration of chaos in molecular kinetics (Gutzwiller 1992) displaying chaotic variation in transition time
[phase]. This supports a model in which molecular complexes form an interface between chaos and quantum
nonlocality as portrayed in the fractal models illustrated in fig 2(d,e).
However it is the stochastic wave-reduction aspect of quantum mechanics which generates the unpredictabilities
found in chaotic physical systems and is the source of randomness in their statistical mechanics. For example
molecular kinetics is made uncertain through diffraction of the wave aspect of a molecule by other molecules. An
amino acid at room temperature has a self-diffraction angle of about 5o (King 1989), contributing initial condition
uncertainty to each successive kinetic encounter when traversing a molecular medium. One of the important roles
of classical chaos may thus be quantum inflation, the amplification of quantum fluctuation into global perturbations
of the dynamic.
8.5 Quantum concepts and consciousness.
Interest in quantum concepts in brain function has had a considerable history Eddington (1935), Szent-Gyorgyi
(1960), Eccles (1970) and Bohm (1980). Wigner (1961), Popper and Eccles (1977) and Margenau (1984) and
among others have suggested that quantum reduction is precipitated by the consciousness of the observer38 .
Quantum decoherence (Zurek 1991) or registering a classical record is also a possibility. Bohm's (1952) work on
the Einstein-Podolsky-Rosen conjecture, the advent of Bell's theorem and the Aspect experiments (Clauser &
Shimony 1978, Aspect et. al. 1982) which display spin-correlations between a split photon pair over space-like
intervals have demonstrated that hidden variable theories cannot be locally-causal, i.e. depend on local interactions
which are transmitted no faster than light.
The possible implications of quantum non-locality for consciousness depend on which interpretation of quantum
mechanics is used. Some theorists who follow the Everett many-worlds interpretation assert that reduction of the
wave packet never occurs and that the universe is continually branching into all of its possible quantum outcomes
which are presumed to co-exist as parallel aspects of a cosmic wave function. In such a view every quantum
calculation is a superposition of overlapping quantum states and the utility of quantum non-locality is reduced to
forming a parallel computer using superimposed states instead of discrete logic.
It has been proposed that Bose-Einstein condensates could function as quantum computers in which correlated
particles could perform a superposition type computation (Zohar 1991, Hameroff 1994). Hameroff has made the
suggestion that microtubules could be a form of quantum computer possibly taking the form of a molecular cellular
automaton. Cellular automata are capable of being formal computers. Deutch (1985) has analysed the potentiality
38
In the Wigner's friend paradox, an observer's friend splits the wave function, and reports on the result. Multiple
minds thus lead to ambiguities of splitting. One way around this paradox is to require mind to be a cosmic unity,
another is that the first conscious observer in the chain collapses the wave function.
Page 18
of a quantum computer utilizing superposition of states. Although several instances have been given in which a
quantum computer might solve specific tasks more efficiently, (Lockwood 1989) there do not appear to provide
qualitative advantages over parallel distributed processing.
The many-worlds interpretation contradicts the evidence of our conscious sensory processes which experience only
one of the possible outcomes thus conforming to a single historical process. Other approaches depend directly of
collapse of the wave packet. The mathematician Roger Penrose (1986,1989) has suggested that collapse of the
wave function may be a deterministic process based on the interaction of the superimposed wave function with the
gravitational field at the level of one graviton. He has also postulated the idea of non-locality correlating the
activity of various parts of the brain (Penrose 1987). The supercausal model proposed earlier in this paper, 5.2 is
similarly based on quantum reduction.
8.6 The transactional interpretation of quantum mechanics
The supercausal model is based on the transactional interpretation, which developed out of Feynman’s absorber
theory (Davies 1974), is a form of special-relativistic quantum mechanics, utilizing the Feynman propagator
diagram, fig 4.
The basis of the transactional interpretation is that each real and virtual particle can exist only as a link between
emission and absorption foci, as an instance of the self-interaction of the universe, and consequently that particles
cannot be created only to disappear into empty space. It is consistent with the behaviour of all virtual particles
which mediate the quantum fields of the fundamental forces such as electromagnetism and the nuclear forces, and
gravity, because each virtual particle must have an emission and an absorption focus to ensure it exists only within
the limits set by quantum uncertainty (18). It is also consistent with Feynman diagrams in which a particle
travelling in the usual (retarded) direction can be equated with its anti-particle in the time-reversed (advanced)
state. Time reversal is standard in Feynman diagrams, a time-reversed electron being equivalent to a positron fig
4(e)39 . For a photon, which is its own anti-particle, these reduce to offer and confirmation waves of the emission
and absorption foci.
The relativistic energy-momentum equation
E2 = p2 + m2
has two solutions
E =±
2
p+m
[8.6.1]
2
[8.6.2]
in which the negative energy solution has reversed temporal behaviour in space-time.
Hamiltonian equation, 8.3.1 for a zero spin particle with mass m has elementary solutions:
j+,k = (2p)-3/2
where
e i (k.x - wt)
For example, the
[8.6.3a]
j- ,k = (2p)-3/2 e - i (k.x - wt)
[8.6.3b]
w= ( k2+ m2)1/2
[8.6.4]
In the transactional interpretation of quantum mechanics (Cramer 1986) fig 4(d), a mutual encounter between
emitter and absorber is modelled by the release of crossed-phase advanced and retarded waves, each having zeroenergy, the offer wave of the emitter and the confirmation wave of the absorber. The retarded portion of the offer
wave travels with increasing time in the usual manner permeating space-time and meeting potential absorbers.
Each potential absorber in turn releases a confirmation wave. The advanced portions of the confirmation waves
back propagate in time, meeting simultaneously at the emission vertex. Collapse now occurs so that one absorber is
associated with the emitter. The mutual interference of these advanced and retarded waves produces a real
superposition (the photon) between the emission and absorption events in space-time. Transaction is represented
also in the fundamental equation, 8.3.2 in which the two wave function terms j and j* represent the offer and
39
This correspondence enabled Dirac to predict the existence of the positron from the negative energy solutions to his
electron wave equation.
Page 19
confirmation waves, the * [complex conjugate] arising from time inversion of the advanced confirmation wave.
In the Feynman diagram fig 4(b), the force between electrons is determined by integrating all possible virtual
photon and higher-order interactions (c). The photon is virtual because it exists only for an interval consistent with
the uncertainty relations, 8.3.3, and is detected only by its secondary effects in the electric field. While in virtual
exchange, the effects of all possible exchanged photons are integrated, in the case of a real photon, the boundary
condition that only one particle is exchanged, forces quantum reduction of the set of all possible exchanges to one
real exchange.
The Aspect experiments illustrate that correlations occur across space-like intervals which cannot be bridged at the
speed of light. The transactional interpretation explains such correlations by the confirmation waves of both
absorbers interfering at the emission focus thus producing a communication by backward referral to the time the
photon was emitted. Transactions are also the basis of the decoherence model of wave function collapse (Zurek
1991).
8.7. Transactions and Quantum Computation
Quantum computation (Brown 1994) has become an exciting issue in physics and computing because it provides
the potentiality to profoundly speed up parallel computational processes, and even possibly provide solutions to
problems which may be classically intractable (Calude and Pavlov 2002). Quantum computational schemes suffer
from the need to maintain isolation from disturbance during calculation, however various consciousness research
programs seek to find biophysical evidence for coherent states and the potential capacity for quantum computation
in nucleic acids and other structures.
The configurations used in posing quantum computational problems such as decryption have features in common
with the configurations one would anticipate the brain using in transactional anticipation, raising the possibility of
these two quantum processes interpenetrating. In a decryption context a set of quantum systems are partially
excited so they enter a superposition of excited and unexcited states. The quantum system is divided into two parts
L and R so that measurement of one part R collapses the other L to a solution to the decryption problem. The
solution in L is then decoded by using quantum parallelism again to convert L into its own discrete Fourier
transform thus displaying its periodicities and giving a pointer to the numerical solution.
Transactional decision making differs from quantum computation in that the boundary conditions, instead of being a
superposition leading to a measurement of a computed solution are a superposition leading to an open-ended
decision which does not have a precise computational answer but rather may anticipate a future state of the brain.
However in other respects, the biological substrates providing capacity for quantum computation and transactional
decision making would strongly overlap providing a potentially common and complementary functional design.
Page 20
Fig 5: (a) Nor-epinephrine and serotonin pathways originating from mid-brain centres modulating light and dreaming sleep are
distributed across wide areas of the cortex (Bloom et. al. 1985). (b) Inputs from different areas impinge on a singe hippocampal
CA1 neuron via distinct neurotransmitters, thus mapping neurosystems architecture on to single cells (Alkon 1989). (c) Looping
circuits of the limbic system are involved in both affect and memory. (d) Limbic structures in brain section (Bloom et. al.
1985).
eye
supplementary
motor cortex
frontal
lips
(i)
visual
Wernicke
silent .. reading .. aloud
Broca
awake
visual
(ii)
*
(a)
counting down .. a walk into town
(b)
(i)
frontal
parietal
occipital
(c)
eyes open
(ii)
REM
REM
(iv)
stage 3 sleep spindle (v)
stage 5
slow delta (vi)
(iii)
100 mV
1 sec
Fig 6: (a) Cortical modularity in PET scans. (i) Silent reading is contrasted with reading aloud, in which there is wider cortical
involvement, including motor and somatosensory lips areas. (ii) Counting down is contrasted with visualizing a walk into town,
stimulating a variety of frontal areas as well as the parietal cortex (P. Roland ex Blakemore 1991). The supplementary motor
cortex is activated in all four views. (b) Similarity of the REM sleep EEG (iv) to the alert state [(i)-(iii) eyes open]. (c) REM
sleep PET scan parallels the awake brain in activation of visual cortex and frontal lobes [dark], except for reduced REM inferior
frontal activity (*), consistent with the lack of control in dream sequences.
9 Appendix C : The neurophysiological basis of mind
The experience of consciousness requires the global participation of the active brain. The ‘graceful degradation’ of
function and subjective awareness that results from damage to a variety of cortical areas (Blakemore 1991) suggests
the mind arises from distributed brain processes, rather than a specialized area. The major structures in the brain
will be examined to indicate how each contributes to a global dynamical system representing the active conscious
state.
Page 21
9.1 Modular representations on the cortex.
Many different aspects of conscious experience can be associated with transform processing in which primary
sensory inputs are transformed into an envelope of features including oriented lines, binocular dominance and the
homunculus representing the body in the somatosensory cortex (Fodor 1983, Mountcastle 1978).
A variety of
experiments confirm features such as written and spoken language, music, faces, spatial orientation etc. are all
localized in a modular way, sometimes lateralized predominantly in one hemisphere, as is the case for language.
Visual processing is clearly modular, with line orientation columns, and parallel processing of colour and
movement in distinct areas (Zeki 1992). It remains unclear how these modular aspects are reintegrated except by
diffuse connections as they have no common projection area. The PET scans in fig 6(a) illustrate the
correspondence between different conscious activities and the activity of specific modular regions of the cortex,
including Wernicke's and Broca's areas of linguistic interpretation and articulation, the supplementary motor
cortex, and areas in the frontal lobes. Listening to ambiguous signals [time reversed recordings] can activate a
majority of the cortex (Friberg 1992) suggesting activation is a product of instabilities in the process of forming a
representation.
Such studies support a modular distributed internal model, which may also be like a hologram in its use of
distributed phase fronts and wave transforms. This aspect arises naturally from the many to many nature of
synaptic connections, the simultaneity of the Hebbian response and the decomposition of sensoria into modular
characteristics, forming a parallel representation in which each experience or memory is registered across the cortex
in terms of its attributes.
9.2 Ascending distributed pathways.
A very important contribution to conscious activity comes from the distributed pathways ascending from the
midbrain centres responsible for general arousal in the reticular activating system, and in regulating the modes of
wakefulness, light and dreaming sleep. Two pathways, fig 5(a), involving the [inhibitory] neurotransmitters
serotonin and nor-epinephrine, lead from the Raphe Nuclei and the Locus Coeruleus to diverse cortical areas.
Methylated serotonin and catecholamine analogues constitute key hallucinogens. The onset of dreaming sleep is
heralded by activity of cells in the Pons and silencing of cells in the Raphe Nuclei and Locus Coeruleus (Bloom et.
al. 1985). Similar dopamine paths spread out from the Substantia Nigra into the frontal lobes and motor centres.
Dreaming sleep is one of the most singular phases of conscious activity in which feedback appears to be
accentuated at the expense of external input, generating complete subjective realities. The nature and function of
dreaming consciousness and its wealth of detail remains obscure. Dreaming states provide active PET scans and
EEGs similar to the waking state, fig 6(b,c), reflecting the conscious intensity of dream experiences. One difference
in dreams which may reflect their uncontrolled nature is the lower activity of the inferior frontal cortex (Madsen
et.al. 1991). Hallucinogen action may also occur through the ascending distributed pathways, giving them the
capacity to modulate excitability across the entire cortex. Alongside dreaming, they are responsible for some of the
most remarkable changes discovered in the nature of consciousness.
9.3 The limbic system.
The limbic system fig 5(b-d), (Mishkin et.al.1988, Alkon 1989) forms a set of looping pathways combining
sensoria, emotional states and episodic long-term memory. The hippocampus, which has an older three-layered
structure than the six-layer neocortex has a pivotal role in long-term memory. It has projections from diverse
sensory areas via the entorhinal cortex and feeds back into the thalamus and subsequently to cortical areas including
prefrontal, cingulate gyrus, and basal forebrain (c). The amygdala has similar looping circuits linking sense modes
and connecting to the thalamus and deeper emotional centres in the hypothalamus. Phase decoherence occurs in
the hippocampus during orientation to unfamiliar stimuli. The limbic system thus forms a bridge between emotion,
memory and representation of actions and goals in the frontal lobes, consistent with the emotional and motivational
side-effects of frontal lobotomy and studies on time-delayed learning in damaged hippocampi.
9.4
The frontal cortex : Time and intentional action.
The frontal cortex forms representations of activities in time integrating future intentions and goals into timedirected actions based on past experiences. These may involve immediate memory, the central survival strategies
figuratively described as the super-ego, and the capacity to anticipate and predict events in motion. Thus the frontal
cortex may generate a spatially distributed representation of time in terms of the organization of both remembered
Page 22
and planned actions spanning the past and future, utilizing oscillatory phase relations as seen in EEG and evoked
potential studies.
Immediate short-term memory appears to be centred on the prefrontal cortex with reciprocal connections with both
the parietal cortex and the limbic system. Prefrontal damage effects use of knowledge to guide behaviour in
everyday situations, including predictive tracking e.g. of projectile movements (Goldman-Rakic 1992). When a
monkey is trained to look at where a target has disappeared after a delay, selected cells in the prefrontal cortex fire
on the target disappearing, others fire during the delay and others on the motor act. Such eye movement also
involves feedback loops to the basal brain. Prefrontal action is modular with spatial and compound attributes active
in different loci.
9.5 Global dynamics : Mind states and brain states.
Examination of the contributions to consciousness by the major structures of the brain confirms that all are required
in interaction for consciousness as we know it to occur. This suggests that consciousness is a global product of the
brain as a dynamical system. The reciprocal linkages between the cortex and thalamus provide for active dynamical
coupling. Energetic activation by the ascending distributed pathways is essential for consciousness and function of
the cortical dynamical system. These pathways play the role of adjusting parameters which can take the cortex
through various modes of conscious activation or coma. The sensory and associative areas of the cortex can be seen
to contribute in a modular manner to the envelope of features of conscious experience, representing both perception
and action in time. The looping circuits of the limbic system are structured to provide feedback between cortical
areas involved in emotional tone, sensory integration and accessing past experiences. The hippocampus appears to
provide additional parameters which subsequently enable serial access to past experience in relation to a current
stimulus. The major anatomical structures in the brain have their natural explanation in the way they form a global
dynamical system whose interactive states correspond to our conscious awareness. The global dynamical system
also explains the binding problem, the unitary nature of consciousness in a parallel distributed brain.
10 Conclusion
The importance of developing a model of brain function which gives a consistent description of mind,
consciousness and free-will, is profound. The brain may provide a unique manifestation of the supercausal aspect
of quantum reduction as a result of its unique connectivity, coherence and chaotic sensitivity. Cosmology is not
simply a matter of vast energies, but also quantum laws. The diversity of wave-particles resulting from symmetrybreaking of the four fundamental forces finds its final interactional complexity in molecular systems, ultimately
realized in the most delicate and complex of molecular systems known - the conscious brain. The brain may thus be
a doorway between two complementary aspects of the physical universe, the time-directed nature of cosmic
symmetry-breaking and the time-symmetric nature of the sub-quantum domain (King 1989). If so, consciousness
and mind-brain duality may be central to cosmology.
It seems Einstein’s god has had the foresight
to play with predictive dice. C.K.
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